A096258 - OEIS

%I #12 Jul 25 2015 19:34:17

%S 1,1,0,0,1,1,1,1,1,2,3,2,2,3,4,5,5,4,6,8,8,9,11,11,13,16,17,19,22,23,

%T 27,31,32,36,43,47,52,57,61,70,80,84,93,105,114,127,141,150,167,188,

%U 202,220,244,264,291,322,346,377,416,450,493,540,580,633,696,750,814,888

%N Number of partitions of n into distinct nonprime parts.

%H Alois P. Heinz, <a href="/A096258/b096258.txt">Table of n, a(n) for n = 0..1000</a>

%F G.f.: Product_{i>0} (1+x^i)/(1+x^prime(i)).

%p b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,

%p        b(n, i-1)+ `if`(i>n or isprime(i), 0, b(n-i, i-1))))

%p     end:

%p a:= n-> b(n$2):

%p seq(a(n), n=0..70);  # _Alois P. Heinz_, May 29 2013

%t CoefficientList[ Series[ Product[(1 + x^n)/(1 + x^Prime[n]), {n, 70}], {x, 0, 67}], x] (* _Robert G. Wilson v_, Aug 02 2004 *)

%o (Haskell)

%o a096258 = p a018252_list where

%o    p _      0 = 1

%o    p (k:ks) m = if m < k then 0 else p ks (m - k) + p ks m

%o -- _Reinhard Zumkeller_, Jan 15 2012

%Y Cf. A002095.

%Y Cf. A204389.

%K easy,nonn

%O 0,10

%A _Vladeta Jovovic_, Jul 31 2004

%E More terms from _Robert G. Wilson v_, Aug 02 2004